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Math Help - monotonic or not?

  1. #1
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    monotonic or not?

    my teacher was explaining to determine if

    4-(1/n) is monotonic you do the following....


    (1/n) ? (1/n+1)

    (n) ? (n+1)

    (n) < (n+1)

    0 < 1

    ok....so i have this...what does this tell me?
    1. what tells me this is monotonic?
    2. what tells me this is bounded?
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  2. #2
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    First you have to know what n is. n basically is a "natural" number, meaning from 1,2,3,4...

    Now, when n=1, you have 1/n = 1/1 = 1
    when n=2, you have 1/2
    when n=3, you have 1/3, and so on...

    What do you notice? You should that 1/n gets smaller as n gets bigger right?

    Now, what does do for 4-1/n? As n gets bigger, what would happen to 4-1/n?

    What your teacher is trying do is to get you to understand the relationship between 1/n and 1/(n+1), well, think about it, which one should bigger? That would tie in with above.

    Now, monotonic sequence is basically a sequence such that it always decrease, increase, or remain constant as n gets bigger, so what do you think 4-1/n is?

    Now, bounded simply implies that a sequence is "bounded" by a certain value, like 1/n itself will decrease, but it will never get as low as 0, in other words, 0 is greater than or equal to 1/n
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